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Calculus 3 Exam 1
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The general equation x
^{2}
/a
^{2 }
+ y
^{2}
/b
^{2}
+ z
^{2}
/c
^{2 }
=1 represents?
An ellipsoid
The general equation z/c = x
^{2}
/a
^{2 }
+y
^{2}
/b
^{2 }
represents?
Elliptic paraboloid
The general equation z
^{2}
/c
^{2 }
= x
^{2}
/a
^{2 }
+ y
^{2}
/b
^{2 }
represents?
A cone
The general equation z/c = x
^{2}
/a
^{2}
 y
^{2}
/b
^{2}
represents?
A hyperbolic paraboloid
The general equation  x
^{2}
/a
^{2 }
 y
^{2}
/b
^{2 }
+ z
^{2}
/c
^{2 }
= 1 represents?
A hyperboloid of 2 sheets
The general equation x
^{2}
/a
^{2 }
+ y
^{2}
/b
^{2 }
 z
^{2}
/c
^{2 }
= 1 represents?
Hyperboloid of 1 sheet
How do you add and subtract vectors?
Place tiptotail in their respected directions and draw a new vector originating from the first vector's origin.
How do you find th vector between two points?
Take the new components minus the old components.
When are two vectors orthogonal?
If and only if their dot product = 0.
How do you find the angle between two vectors?
Cos(
) = a
b / a b
What are the direction cosines?
Cos(
) = a
_{1 }
/ 
a

Cos(
) = a
_{2 }
/ a
Cos(
) = a
_{3}
/ a
a
is the vector itself
What is the scalar projection?
Comp
_{a}
b
= a
b / a
What is the vector projection?
Proj
_{a}
b
=( a
b / a
^{2}
)a
How do you find the magnitude of a vector?
(X)
^{2}
+ (y)
^{2 }
+ (z)
^{2 }
a
X
b
is _________ to both
a
and
b
.
Orthogonal
When are two vectors parallel?
Ifand only if their cross product = 0.
How do you find the area of a parallelogram created by two vertices?
Find the cross product of them, then take the magnitude of it.
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Author
AnnaRinaldo
ID
238368
Card Set
Calculus 3 Exam 1
Description
Section 13.1  14.2
Updated
20131002T18:59:01Z
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